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is used when turbulence is to be modelled. The constant C 3ε in the ε equation is then set equalto 0.2 as recommended for stable stratification [3]. Bathymetry is modelled using cellporosity.The bottom surface stress (first study case only) is included as a source (S 1 ) for the horizontalmomentum equation with a value calculated using the flow velocity u 1 at 1m from the seabottom and a drag coefficient C D of 0.0025 [4]. The values k sb , ε sb at the grid node distance y sbfrom the sea bottom are calculated from expressions assuming equality of production anddissipation of turbulence (the equilibrium assumption, [5]), giving3S12( )1 S1ρS1= −CDρu1u1, ksb= , εsb=0.3 ρ 0.4ysbField values of k, ε , when turbulence is modeled, are initialised at t=0 to 10 -6 (m 2 /s 2 ) and10 -9 (m 2 /s 3 ) respectively. Initial waveforms are prescribed in the domain from mathematicalapproximations or measured values. The ocean surface is represented as a rigid free slip lid togood approximation since the surface elevations induced by internal waves are smallcompared to the internal wave amplitude. The lateral boundaries can be either inflow oroutlow (fixed ambient hydrostatic pressure) for the first case or cyclic for the second case.CASE STUDIES1. Large amplitude, shoaling internal waves in the South China SeaLarge amplitude internal waves are a common feature of the World’s oceans and arefrequently observed near regions of rapidly varying topography where tidal forces distortstable ocean stratification. Internal waves are important because they cause distortion ofacoustic propagation paths, and produce localised current pulses which can affect drillingoperations, submersible stability and water clarity due to sediment resuspension.Recent measurements taken as part of the Office of Naval Research (ONR) sponsored AsianSeas International Acoustics Experiment (ASIAEX, 2001) in the South China Sea haveprovided detailed in situ evidence of many internal wave features previously inferred fromsatellite or theory. Relevant internal wave results from this experiment are reported by Orr andMignerey [6] who show observations of internal waves of depression propagating intoshallow water transformed into internal waves of elevation, a process that was expected fromtheory (Grimshaw [7]) and suggested by Liu [8] from satellite images.PHOENICS has been used to simulate the propagation of large amplitude internal wavesacross water depths from 260m to 100m. The aim has been to assess the capability of a CFDcode to reproduce the essential characteristics of the internal wave phase speed, shape and ,localised currents by comparison with the observations from ASIAEX. The details of thelocation and ship track during the measurement programme of ASIAEX are shown in Figure1. The background stratification is taken from Conductivity, Temperature and Depth (CTD)2
profiles taken during the experiment. Figure 2 shows the resultant averaged density profile. Astrong pycnocline is evident between 40 and 80 m depth.The simulation uses a bathymetric slope of gradient 1 in 125 preceded by a flat bottom sectionof depth 260m. The latter section is sufficiently long to enable the initial, approximateKorteweg de Vries (KdV) internal solitary wave (which does not fully satisfy the full nonlinearequations) to transform into a nearly steady solitary wave solution of the CFD model. Inprinciple a more accurate initial condition could have been incorporated from the ASIAEXmeasurements themselves but these were not available at the commencement of thecomparison exercise. The initial waveform and range velocity distribution are shown inFigure 3. The CFD model is then used to propagate the solitary wave across the continentalslope from 260m to 100m over 20km using a range grid size of 15m, vertical grid size of 2mand time step of 1.25s. This choice of resolution has been guided by previous simulations,which have given reasonable results [9], [10].Figure 4 shows the results of the CFD shoaling simulation of two solitary waves with initialamplitudes of nominally 70m and 100m (illustrated using the mid density contour in thewave). The simulations show the broadening of the initial wave with a decreasing forwardpropagating slope and the appearance of waves of elevation behind the main forwardlypropagating wave. These elevation waves appear in ~190m deep water for the 100m initialwave and ~175m deep water for the 70m initial wave – the observations record thisoccurrence in water depths between 150m and 180m. The amplitudes of the waves ofdepression decrease in both cases, while the amplitudes of the elevation waves increase.Figure 5 shows a comparison between the predicted phase speed for the 100m wave(considered the more representative of the experimental situation) and measurements made byOrr and Mignerey using specific locations (shown in colour) in the leading wave ofdepression and following depression waves. There is considerable scatter in the experimentalmeasurements depending on which measurement location is chosen. The PHOENICSpredicted phase speed was determined from a point corresponding to the largest amplitude ofthe lead soliton and so should most closely compare with the cyan measurement line. There isreasonable agreement with this measurement which is within the scatter defined bymeasurements using other locations.Figure 6 compares predictions of the model at t=21250s with observations at a similar depthusing an Acoustic Doppler Current Profiler (ADCP). This comparison shows reasonableagreement between the form of the wave profile (both in amplitude and width) and a similardistribution of range velocity in the leading section of the wave and the following elevationwave (which has the reverse circulation). Although the colour scale ranges for the predictedand measured range velocities differ significantly, the actual velocities measured are, in fact,reasonably close to the predicted values (Peter Mignerey, private communication). Note thatthe two velocity measurement peaks occurring to the left of the elevation wave are due toadvancing solitons not considered in this CFD simulation.Figure 7 shows the prediction of the turbulent dissipation rate in the 100m wave at t=21250swhen it is transforming into a wave of elevation. Figure 8 suggests that the highest dissipationrates appear when significant elevation waves are formed – this is perhaps not surprising as3
Page 1: Title: Some applications of PHOENIC
Page 5 and 6: athymetry (first case study) is not
Page 7 and 8: Figure 1. (Top) Bathymetry of South
Page 9 and 10: Figure 3. 100m amplitude wave case.
Page 11 and 12: Figure 5. (Top)Variation of wave ph
Page 13 and 14: Figure 7. (Top) PHOENICS prediction
Page 15 and 16: Figure 9. Turbulent dissipation rat
Page 17 and 18: Figure 11. (Top) Predicted concentr
Page 19 and 20: Figure 13. Malin shelf internal wav

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